The Nikkei Stock Average on Tuesday jumped to a 22-month high as the yen fell, though other Asia-Pacific markets were relatively quiet following a global rally Monday that pushed some indexes in the U.S. and Europe to fresh highs.

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In addition, Federal Reserve Bank of New York President William Dudley expressed optimism on Monday about the U.S. economy. He also signaled a willingness by the Fed to continue raising rates gradually.

"With Dudley perceived as a 'dove' at the Fed, this is an important reaffirmation of Fed intent," said Greg McKenna, chief market strategist at AxiTrader.

U.S. tech heavyweights, which went through a rough patch earlier this month, rebounded on Monday. Apple (AAPL) rose 2.9% after sliding in six of the prior seven sessions.

Taiwan, which is home to a number of Apple suppliers, saw its benchmark index rise. The Taiex added 0.7% to 10,324.46, roughly 70 points away from an intraday high reached in 2000. iPhone maker Hon Hai (2317.TW) rose 4.6% to hit another record. On Monday, the Taiex recorded its highest closing level since 1990.

The Nikkei , which climbed 1.2% over the prior two sessions, rose 0.8% to 20,230.41 on Tuesday, the highest since August 2015 as the yen was broadly weaker. The U.S. dollar remained around Yen111.65 .

After the close of U.S. stock trading, MSCI will say whether it will include some stocks traded in mainland China in its widely followed emerging-markets index. Analysts say sentiment would be lifted in Hong Kong and on the mainland if MSCI decided to include these Chinese stocks.

Australian stocks ended lower Tuesday, with the S&P/ASX 200 index down 0.8%. The country's big banks, which make up about a quarter of the benchmark's weighting, fell nearly 1% after Moody's late Monday downgraded 12 Australian banks due to worries about heavy household borrowings in real estate.